Some are created from magic, whether holy or unholy, and are created for similar reasons as Golems, whereas others are “grown” as an extension of the parent species’ body, and yet others are simply manufactured as weapons.
There are several Bioconstructs featured in various media in which these beings are immensely durable, and capable of taking enormous punishment, for example, Flesh Constructs from the Malifaux universe.
In the case of petroleum, flesh, organic waste constructs and the like, some are capable of consuming whole creatures to enlarge or reconstruct themselves, or increase their natural abilities. For instance, Dark Souls II states that "The Rotten embraces all in the sanctuary for all things unwanted or tossed away." Similarly, the Slime King from Terraria is greater than the sum of its parts
Many Bioconstructs exhibit an unnatural level of physical strength. Possibly the earliest Bioconstruct in literature, the brutish Frankenstein's Monster, was easily capable of lifting a human being without a second thought.
A few Bioconstructs are made from materials that are highly toxic or hazardous to any true living creature. Creatures such as Marvel's Man-Thing has an acutely toxic touch, as it melts skin and flesh from bone.
A number of Bioconstructs can split into two or more organisms to create multiples of themselves.
As mentioned before, various Bioconstructs are capable of absorbing material into themselves either for the purpose of healing their physical form, or for replenishing other, more unworldly, powers.
weak to fire
In the case of fighting a petroleum creature, they may be able to burn.
Weapons such as machine guns or flamethrowers(or anything that can outclass it's regeneration) may be able to be rid of its presence.
On the contrast, why not use weapons that are slow but deal immense damage rather than a weapon that is fast firing that fires weak projectiles? Either type has a slim chance to work.
hitting weak points
As most bioconstructs are crudely made, there may or may not be a design flaw to easily exploit, whether it being a body part being shoddily constructed or a cumbersome design, making the creature horribly slow.